Is zero an even number? (2024)

Superstorm Sandy had many consequences, some easier to foresee than others. Millions experienced floods and power cuts, the New York marathon was cancelled, and pictures of sharks in the city appeared on the internet. Another outcome was to draw attention to the unique position of the number zero.

To deal with fuel shortages after the storm, New York Mayor Michael Bloomberg introduced rationing on 8 November.

"Drivers in New York City who have licence plates that end in an odd number or end in a letter or other character will be able to gas or diesel only on odd-numbered days such as tomorrow which happens to be the 9th," he said.

"Those with licence plates ending in an even number, or the number zero, will be able to buy gas or diesel only on even number days such as Saturday November 10th."

The use of the phrase "even number, or the number zero" implies that zero is not even. On the other hand, the mayor is lumping zero together with the even numbers, so he certainly doesn't think it's odd.

So what is it - odd, even or neither?

For mathematicians the answer is easy: zero is an even number. The rest of us may not feel completely sure.

According to Dr James Grime of the Millennium Maths Project at Cambridge University, reaction time experiments in the 1990s revealed people are 10% slower at deciding whether zero is odd or even than other numbers.

Children find it particularly difficult to recognise if zero is odd or even. "A survey of primary school children in the 1990s showed that about 50% thought zero is even, about 20% thought it was odd and the remaining 30% thought it was neither, both, or that they don't know," explains Dr Grime.

"It appears that we may file numbers mentally into lists such as the even numbers two, four, six, eight or numbers to the power of two which would include two, four, six, eight or two, four, eight, 16. Zero is not on these lists so it takes us longer to work out."

So why, mathematically, is zero an even number? Because any number that can be divided by two to create another whole number is even. Zero passes this test because if you halve zero you get zero.

Zero also has odd numbers either side of it - minus one and one - and so this is another test it passes to be classified as an even number.

In fact, there is an argument that zero is the most even number of all. A number which is "doubly even" can be divided by two and then divided by two again. Zero can be divided by two forever and the result will always be a whole number - zero.

It's not just the public who have struggled to recognise zero as an even number. During the smog in 1977 in Paris, car use was restricted so that people with licence plates ending in odd or even numbers drove on alternate days.

"The police did not know whether to stop the zero-numbered licence plates and so they just let them pass because they didn't know whether it was odd or even," says Dr Grime.

It even took mathematicians some time to agree on the question.

To begin with, zero was not recognised as a number at all. The Babylonians and the Ancient Greeks used it to differentiate between small and large numbers, for example 26 and 206. Before this, people could only tell if one number was bigger than another by the context in which it was used.

In the 13th Century, the Italian mathematician Fibonacci was the first to popularise Arabic numerals, the numbers that we use today, in Europe. He classified one to nine as numbers but zero as a "sign".

The struggle they had was if zero is nothing, is it even a number at all and can it have the properties of being a number? For example, oddness or evenness?

"It wasn't until the 1600s that zero was truly accepted as an even number - after resistance and debate," says Grime.

For more than 1,000 years mathematicians had difficulties with the number zero and non-mathematicians are still often uncertain about how to classify it.

So Bloomberg had every reason to spell out to New Yorkers in black and white that he was lumping zero along with the (other) even numbers.

Listen to More or Less on BBC Radio 4 and the World Service, or download the free podcast.

You can follow the Magazine on Twitter, external and on Facebook, external

Is zero an even number? (2024)

FAQs

Is zero an even number? ›

In mathematics, zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. This can be easily verified based on the definition of "even": it is an integer multiple of 2, specifically 0 × 2.

Is zero an odd or even number? ›

Zero is an even number. In other words, its parity—the quality of aninteger being even or odd—is even. The simplest way to prove that zero iseven is to check that it fits the definition of "even": it is an integermultiple of 2, specifically 0 × 2.

Why is 0 not the first even number? ›

Zero is indeed an even number. Whether it is “first” or not just depends on where you start counting. If you start at zero then it is first. If you start at one then it is not.

Why is 0 a number? ›

Zero could be considered a placeholder or a number. Zero is neither positive nor negative and thus it is considered a neutral number. Mathematicians agree zero is a counting number, a whole number, and an integer.

Is 0 the smallest even number? ›

0 is both an even and a whole number. As a result, 0 is the smallest, even whole number.

What type of number is 0? ›

Answer: 0 is a rational number, whole number, integer, and a real number. Let's analyze this in the following section. Explanation: Real numbers include natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Is zero just another even number? ›

Is 0 Even? An even number in mathematics is a number that can be written as n=2⋅k for a whole number k . If k=0 , the equation 0=2⋅k remains accurate. This makes zero an even number.

How to prove that 0 is even? ›

The standard definition of "even number" can be used to directly prove that zero is even. A number is called "even" if it is an integer multiple of 2. As an example, the reason that 10 is even is that it equals 5 × 2. In the same way, zero is an integer multiple of 2, namely 0 × 2, so zero is even.

Is a number ending with 0 even? ›

All the numbers ending with 0, 2, 4, 6 and 8 are even numbers. For example, numbers such as 14, 26, 32, 40 and 88 are even numbers. To identify even numbers, we observe the last digit or the ones digit of the number. If it ends in the digits 0, 2, 4, 6, or 8, then it is an even number.

Is there a proof for zero? ›

You actually don't, in the modern structure of mathematics it exists by definition as the first natural number. We have to start by assuming there exists a number, and then we define all numbers from there. We convince ourselves that it makes sense that numbers exist, but we can't prove it from within the system.

Is 0 a fake number? ›

The number 0 may or may not be considered a natural number, but it is an integer, and hence a rational number and a real number. All rational numbers are algebraic numbers, including 0.

How is 0 a number if it's nothing? ›

Zero is a real number because it is an integer. Integers include all negative numbers, positive numbers, and zero. Real numbers include integers as well as fractions and decimals. Zero also represents the absence of any negative or positive amount.

Is a 0 yes or no? ›

Usually in logic, 1 and 0 are interpreted as True and False, respectively. In non-classical logics with a third truth-value, this is usually interpreted as 'neither true nor false'.

Is 0 technically even? ›

So why, mathematically, is zero an even number? Because any number that can be divided by two to create another whole number is even. Zero passes this test because if you halve zero you get zero.

Is 0 the first even number? ›

The first even whole numbers are: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and so on. Notice in the number line, that between 6 and 8, for example, there isn't any other even number. When this happens, the numbers are called consecutive even numbers. Similarly, 2 and 4, -6 and -4 are consecutive even numbers.

Is 0 an even rational number? ›

Yes, Zero is an even number because the parity of Zero is Even. Any number that when divided by 2 leaves 0 as the remainder is considered an even number. Now, zero when divided by 2 leaves 0 as the remainder, and hence it is considered an even number.

How do you know if zeros are even or odd? ›

If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero. If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity. If the graph crosses the x-axis at a zero, it is a zero with odd multiplicity.

Are 0 and 1 odd numbers? ›

Even numbers are the ones whose units place digit is either 0, 2, 4, 6, or 8, and odd numbers are ones whose units place digit is either 1, 3, 5, 7, or 9. Examples of even numbers are 2, 4, 6, 8, 10, 12, 14, 16, etc, and the examples of odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, etc.

Is 1 an odd no? ›

Yes, 1 is an odd number because it is not divisible by 2.

Is zero a multiple of 4? ›

Zero is a multiple of every number so (among other things) it is an even number. When asked for the “smallest” multiple (for example, the least common multiple), the implication is that only positive multiples are meant.

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